High-performance, low-voltage electroosmotic pumps with molecularly thin nanomembranes

ABSTRACT

Thin pnc-Si membranes operate as high-flow-rate EOPs at low applied voltages. In at least some instances, this may be due to the small electrical resistance presented by the membrane and high electric fields across the molecularly thin membrane. The normalized flow rates of some pnc-Si EOPs may be 20 times to several orders of magnitude higher than other low-voltage EOPs.

FEDERALLY SPONSORED RESEARCH

This invention was made with government support under grant number RZIEB007480 awarded by the National Institutes of Health. The government has certain rights in the invention.

RELATED FIELDS

Electroosmotic pumps (EOPs), such as EOPs used in microfluidics applications.

BACKGROUND

EOPs are a class of pumps in which fluid is driven through a capillary or porous media within an electric field.

Electroosmotic flow results from the interaction between an electric field and the diffuse layer of ions at a charged surface. In capillaries or pores, the migration of the diffuse layer toward the oppositely charged electrode causes the bulk fluid within the channel to flow through viscous drag. In some instances, EOPs may be designed to generate high flow rates in microchannels using these principles. EOPs may, in at least some instances, present a number of advantages over mechanical pumps, including the lack of mechanical parts, pulse-free flows, and ease of control through electrode actuation. In some instances, EOPs have been considered for use as pumps for cooling circuits and microfluidic devices that aid in drug delivery or diagnostics. Microfluidic devices may facilitate the miniaturization of multistep laboratory processes into small, low-cost, disposable units. The inclusion of multiple steps into a single device increases the need for the precision pumping of fluids on-chip.

High voltages (>1 kV) are often required for direct current (dc) EOPs to achieve sufficient flow rates in microchannels. However, devices with high-voltage EOPs require bulky external power supplies and a skilled technician to operate, which may defeat the ease of use and portability aims of a microfluidic diagnostic tool in some instances. Recently, low-voltage EOPs have been fabricated from porous silicon, alumina, track-etched polymer, and carbon nanotube membranes. These low-voltage EOPs are much thinner than their high-voltage predecessors (60-350 μm compared with >10 mm), but still have drawbacks.

SUMMARY

Thin pnc-Si membranes operate as high-flow-rate EOPs at low applied voltages. In at least some instances, this may be due to the small electrical resistance presented by the membrane and high electric fields across the molecularly thin membrane. The normalized flow rates of some pnc-Si EOPs may be 20 times to several orders of magnitude higher than other low-voltage EOPs.

In one non-limiting example, a micro-fluidics device may include a micro-fluid input, a micro-fluid output and an electroosmotic pump in fluid communication with the micro-fluid input and output, the electroosmotic pump including a nano-porous membrane having a thickness of 2-100 nm, the electrosmotic pump configured to move a fluid through the nano-porous membrane from the micro-fluid input into the micro-fluid output.

In this non-limiting example, the nano-porous membrane may include pores having widths in the range of 2 nm-100 nm.

In this non-limiting example, the thickness of the nano-porous membrane may be in the range of 5-40 nm.

In this non-limiting example, the nano-porous membrane may be a nano-porous membrane comprising silicon.

In this non-limiting example, the nano-porous membrane may be a nano-porous membrane comprising silicon nitride.

In this non-limiting example, the nano-porous membrane may be a porous nanocrystaline silicon membrane.

In this non-limiting example, the electroosmotic pump may include a substrate, a passage extending through the substrate, and the porous nanocrystaline silicon membrane being over the passage extending through the substrate.

In this non-limiting example, the micro-fluidics device may also include a plurality of passages extending through the substrate and one or more porous nanocrystaline silicon membranes over the plurality of passages.

In this non-limiting example, the substrate may be a silicon substrate.

In this non-limiting example, the electroosmotic pump may be configured to move the fluid through the nano-porous membrane at an applied voltage between 10 mV and 50 V.

In this non-limiting example, the nano-porous membrane may have a zeta potential of approximately -5 mV to -40 mV.

In this non-limiting example, the nano-porous membrane may have a zeta potential of approximately 100 mV to -100 mV.

In this non-limiting example, the micro-fluidics device may also include a fluid channel extending from the micro-fluid output, wherein the nano-porous membrane has an active area that is at least 25% of a cross-sectional area of the fluid channel.

In this non-limiting example, the active area may be at least 75% of the cross-sectional area.

In another non-limiting example, a micro-fluidics device may include a micro-fluid input, a micro-fluid output and an electroosmotic pump in fluid communication with the micro-fluid input and output, the electroosmotic pump including a nano-porous membrane having a thickness of 2-100 nm, the electrosmotic pump configured to move a fluid through the nano-porous membrane from the micro-fluid input into the micro-fluid output at a flow rate of 50-800 mL·min⁻¹·cm⁻²·V⁻¹, wherein cm corresponds to an active area of the nano-porous membrane and V corresponds to a transmembrane voltage of the nano-porous membrane.

In this non-limiting example, the electrosmotic pump may be configured to move the fluid through the nano-porous membrane from the micro-fluid input into the micro-fluid output at a flow rate of 100-500 mL·min⁻¹·cm⁻²·V⁻¹.

In another non-limiting example, a method of moving a fluid in a micro-fluidic device, the micro-fluidic device including a micro-fluid input, a micro-fluid output and an electroosmotic pump comprising a nano-porous membrane having a thickness of less than 100 nm in fluid communication with the micro-fluid input and output, the method may include: applying a voltage of less than 50 V across the nano-porous membrane; and in response to the applied voltage, moving a fluid through the nano-porous membrane at a normalized flow rate of 50-800 mL·min⁻¹·cm⁻²·V⁻¹, wherein cm corresponds to an active area of the nano-porous membrane and V corresponds to a transmembrane voltage of the nano-porous membrane.

In this non-limiting example, the nano-porous membrane may include pores having widths in the range of 2 nm-100 nm and the thickness of the nano-porous membrane is in the range of 5-40 nm.

In this non-limiting example, applying the voltage may be applying a voltage of less than 1 V across the nano-porous membrane.

In another non-limiting example, a micro-fluidics device may include a fluid reservoir, a sample input, and an electroosmotic pump in fluid communication with the fluid reservoir and the sample input, the electroosmotic pump including a nano-porous membrane having a thickness of 2-100 nm, the electrosmotic pump configured to move a fluid from the fluid reservoir through the nano-porous membrane to move a sample from the sample input through a portion of the micro-fluidics device.

In another non-limiting example, a micro-fluidics device may include an electroosmotic pump, a cooling fluid, a heat source, and a heat sink, the electroosmotic pump including a nano-porous membrane having a thickness of 2-100 nm, the electrosmotic pump configured to move the cooling fluid past the heat source and to the heat sink.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 schematically shows an example of a micro-fluidics device including an EOP.

FIG. 2 schematically shows an example of another micro-fluidics device including an EOP.

FIG. 3 shows four examples of porous nanocrystalline silicon (pnc-Si) chips with one, three, six, or nine 200×200-μm windows of freestanding membrane. A 15-nm-thick pnc-Si membrane extends over each window on the silicon chips.

FIG. 4 shows in cross-section a pnc-Si membrane over a window extending through a silicon substrate.

FIG. 5 shows a transmission electron micrograph image of a pnc-Si membrane.

FIG. 6 graphically illustrates pore diameters distribution of the membrane of FIG. 5.

FIG. 7 shows an electroosmosis testing device. pnc-Si chips are sealed between two PET chambers, and a dc power supply maintains a constant voltage across two Pt electrodes. KCl solution that flows into the receiving chamber was continuously removed and weighed at intervals to determine electroosmosis rate.

FIG. 8 graphically illustrates electroosmotic transport of KCl measured over time for untreated pnc-Si chips with active areas shown in FIG. 3. All measurements were performed at an applied voltage of 20 V. Dotted line indicates a nine-window chip without pnc-Si material.

FIG. 9 graphically illustrates electroosmotic flow rates of untreated pnc-Si membranes as a function of active area at an applied voltage of 20 V. Theoretical points are calculated using the pore characteristics, current, and zeta potential of the particular experimental point.

FIG. 10 shows a streaming potential testing device. pnc-Si chips are sealed between two threaded polycarbonate chambers. Ag/AgCl electrodes measure voltage difference between cells as KCl is pressurized through chamber.

FIG. 11 is an image of the polycarbonate device of FIG. 10. Ag/AgCl electrodes are threaded into a small piece of silicon cording and are compressed into the end of each chamber with polycarbonate screws. Each chamber is filled with KCl and the membrane chip is recessed into one of the chambers between two O-rings. The chambers are threaded together, and excess KCl leaves through the pressure inlet/outlet. A KCl reservoir is attached to the pressure inlet and pressurized by compressed N₂. The potential difference between the two chambers is measured with a voltmeter.

FIG. 12 is a plot of streaming potential vs. pressure data for native and modified membranes. The offset in the y intercept is caused by slight differences in Ag/AgCl wires and chamber assembly. The slope of these curves can be used to determine the zeta potential using Eq. 6 (discussed below). Note that in solving for the zeta potential in this example we use an average pore radius for a. This is because the streaming potential relationship is not additive in this particular example and cannot be easily determined for a pore distribution.

FIG. 13 is a plot of electroosmotic transport of modified pnc-Si membranes. In this particular example, higher flow rates are observed for oxidized membrane. In this particular example, amino silanization reduces the flow rate, but does not change the direction of the flow.

FIG. 14 charts zeta potential measured through electroosmotic (EO) and streaming potential (SP) experiments. In this instance, oxidation increases the zeta potential whereas amino silanization reduces the zeta potential.

FIG. 15 charts pnc-Si electrical resistance. Resistance of pnc-Si membranes is compared with identical form factor chips with windows lacking freestanding pnc-Si material. In this particular example, pnc-Si membranes impart negligible resistance to the system. The “no chip” bar indicates the resistance of the system lacking a silicon chip. The inset of FIG. 15 shows a typical I-V curve from a six-window (0.24-mm2 active area) pnc-Si chip. Error bars are SDs.

FIG. 16 is a table of normalized electroosmotic flow rates for some examples of low-voltage EOPs.

FIG. 17 shows an example of an EOP prototype pump using a polycarbonate housing that seals a circular pnc-Si membrane chip between two viton O-rings. Silver wire electrodes were wound to produce more surface area and painted with AgCl. Tubing with a 1-μm diameter was attached to the inlet and outlet ports of the device.

FIG. 18 shows the EOP prototype pump of FIG. 17 driven with a constant-current circuit that switched polarity using a relay (on breadboard). The flow rate was visualized by filming the movement of the solution front in the tubing under a dissection microscope.

FIGS. 19-21 show screen captures from the film of the EOP prototype pumping in FIG. 18, showing the prototype pumping fluid. The inlet and outlet tubes are shown side by side, and the fluid is moving left toward the negative electrode in the bottom tube (current 0.6 mA, voltage 2.05 V changing polarity every 30 s; scale, mm). FIG. 19 shows a screen capture at 15s and FIG. 20 shows a screen capture at 30s. The fluid has moved 1.5 mm in the 15s between images FIGS. 19 and 20. FIG. 21 shows a screen capture at 55 s. The polarity has changed at this point and the fluid is flowing left toward the negative electrode in the top tube.

FIG. 22 charts voltage during the time span of the FIG. 19-21 screen captures and volumetric flow rate as calculated from individual screen captures during that time span.

FIG. 23 shows a comparison of flow rate under applied pressure. In this example, electroosmotic volumetric flow rate was measured under regulated air pressure in the micro-EOP prototype of FIG. 18 for three applied voltages and a single direction through the EOP. The applied pressure reduces the flow rate and stalls electroosmotic flow in the range of 0.5-1.5 kPa for voltages 1,000-1,500 mV.

FIG. 24 plots normalized volumetric flow rate (Q/Qmax) against normalized pressure (P/Pmax). The plotted solid line represents Eq. 8 (discussed below).

FIG. 25 is a table of electroosmotic flow through examples of 15- and 30-nm pnc-Si membranes under back pressure.

FIG. 26 is a table of hydraulic permeability of examples of 15- and 30-nm pnc-Si membranes.

DETAILED DESCRIPTION OF DRAWINGS

We have developed an electroosmotic pump that includes a nanoporous membrane that, in some instances, may be more than two orders of magnitude thinner than membrane materials previously used in an EOP. Such pumps could be used for portable microfluidic devices, cooling circuits, precision fluid (drug) delivery systems, or for other uses. Such pumps may facilitate high electroosmotic flow rates for low voltages.

In one embodiment, the membrane is an ultrathin (e.g. in a range of 2-100 nm, 10-60 nm, or 15-30 nm in various non-limiting examples) nano-porous membrane material called porous nanocrystalline silicon (pnc-Si). pnc-Si membranes may be fabricated on silicon- or silica-based platforms, or other platforms. pnc-Si membranes may be fabricated on silicon nitride platforms in one non-limiting example. pnc-Si membranes may be fabricated using techniques standard to the microelectronics industry. In some examples, the silicon platform enables control of freestanding membrane area and industrial-scale manufacturing. U.S. Pat. No. 8,152,290, issued May 22, 2012 to Striemer et al., the entire contents of which are hereby incorporated by reference, describes non-limiting examples of methods of manufacturing pnc-Si membranes. FIG. 4 schematically shows in cross section a pnc-Si membrane over a single window extending through a silicon substrate.

Pore distributions in pnc-Si membranes may be controlled in some instances by fabrication temperatures and ramp rates during a rapid thermal crystallization step. Pores can be directly viewed in the ultrathin membrane and characterized with transmission electron microscopy (TEM). Such pnc-Si membranes may exhibit little resistance to the diffusion of small molecules and may have high permeability to water and air.

We have developed EOPs incorporating pnc-Si membranes that exhibit high electroosmotic flow rates at low applied voltages, which may be due to the high electric fields achieved over the ultrathin membranes. In one non-limiting example, such an EOP has been shown to pressurize fluid through 0.5 mm diameter capillary tubing at voltages as low as 250 mV. In another non-limiting example, an EOP with a low active area (0.36 mm²) generates electroosmotic flow rates of 10 μL/min at voltages of 20 V or lower. In some instances, an EOP may generate electroosmotic flow rates at voltages of 250 mV to 20 V. In some instances, an EOP may generate electroosmotic flow rates at voltages as low as 10 mV. In some instances, an EOP may generate electroosmotic flow at voltages in the range of 10 mV to 20 V.

As discussed further below, these flow rates may be compared with electroosmotic theory by calculating electroosmotic flow using pore distributions from TEM micrographs. As also discussed below, surface modifications in some instances may change the zeta potential of the material and influence the electroosmotic flow rates. Surface modifications, such as plasma oxidation or silanization, can influence the electroosmotic flow rates through pnc-Si membranes by alteration of the zeta potential of the material. Non-limiting embodiments of the present invention may provide ultralow voltage and on-chip pumping in microfluidic systems with low back pressures (for example, without limitation, at backpressures of 0.3-4 PSI).

In some examples, the thermodynamic efficiency of a pnc-Si EOPs may be low, such as less than 0.01% due to low stalling pressures. In other examples, the thermodynamic efficiency may be improved orders of magnitude by bringing the electrodes closer to the membrane and reducing the applied voltage.

FIG. 1 shows one non-limiting and schematic example of a microfluidic device (in this instance, a “Lab-on-a-Chip”) including a pnc-Si EOP. Microfluidic devices like the one shown in FIG. 1 may be made of glass, silicon, polymer (e.g. PDMS), or another material. In the particular example shown in FIG. 1, a fluid reservoir 10 connects through a micro-fluid channel to a micro-fluid input of the EOP 12. The EOP 12 may be used to push a fluid from the fluid reservoir 10 through a micro-fluid output of the EOP 12 and down-stream micro-fluid channels in order to, for instance, drive a sample introduced into the micro-fluidics device at sample injection port 14. Using the EOP 12, the sample may be driven to, through, past, or otherwise relative to other units of the micro-fluidics device, such as the filter 16 and sensor 18 shown in FIG. 1 or other units such as mixers, binding sites, or other microfluidic components. In some instances, sample injection port 14 could be located upstream of the EOP 12 instead of downstream. FIG. 1 is just one example of how an EOP could be incorporated into a microfluidic Lab-on-a-Chip, and many other configurations are possible.

FIG. 2 shows one non-limiting and schematic example of a microfluidic cooling circuit including a pnc-Si EOP. In this example, the EOP 20 is connected by microfluidic inputs and outputs to a microfluidic circuit, and pumps fluid from a reservoir 22 to a CPU 24 (or other object to be cooled) and then to a heat exchanger 26 or radiator to cool the fluid.

Experimental and theoretical analyses demonstrate the feasibility and advantages of using non-limiting embodiments of EOPs incorporating pnc-Si membranes.

Methods

pnc-Si Fabrication: The non-limiting examples of pnc-Si membranes in the below described studies were made on 200-μm-<100> silicon-thick wafers using the methods described in Striemer et al. (2007) Charge-and sized-based separation of macromolecules using ultrathin silicon membranes, Nature 445(7129):749-753 (the entire contents of which are hereby incorporated by reference). The photoresist was spin-coated on the surface of the wafers, and chrome masks were used to define the geometry of the 6.5-mm-diameter experimental chips and 3-mm-diameter imaging chips. The masks also defined the intended internal windows of freestanding pnc-Si membranes (one, three, six, or nine windows of 200×200 μm or two slits of 2 mm×100 μm for experimental chips and four windows of 100×100 μm for imaging chips). A three-layer 20-nm SiO₂/15- or 30-nm amorphous Si/20-nm SiO₂ stack was sputtered onto patterned wafers via rf magnetron sputtering. The wafers were annealed at 1000° C. at a rate of 100° C/s to induce crystallization and form nanopores in the reorganized silicon film. The bulk patterned silicon was anisotropically etched with ethylene diamine pyrocatechol, and protective oxide layers were removed with buffered oxide etchant. Pore distributions were obtained from TEM micrographs using an open-source MATLAB (The MathWorks) image processing program (http ://nanomembranes .org/resources/software/).

FIG. 3 shows pnc-Si chips with one, three, six, or nine 200×200 μm windows of freestanding membrane. FIG. 3 shows the active area (area of freestanding membrane) above each chip. A 15-nm-thick pnc-Si membrane extends over each window on the silicon chips, as shown schematically by FIG. 4.

FIG. 5 shows a TEM of a pnc-Si membrane. In FIG. 5, white spots are pores and black regions are diffracting nanocrystals. FIG. 6 graphically illustrates pore diameters as determined by MATLAB image processing of a 1.7×1.1-μm TEM image of the membrane depicted in FIG. 5.

Plasma Oxidation and Aminosilanization: for some of the below described studies, pnc-Si chips were oxidized using a 1224-P Yield Engineering Systems chemical vapor deposition (CVD) system with plasma capabilities. pnc-Si chips were placed in the 150° C. chamber and a vacuum of 0.3 Torr was drawn. A plasma of 0.198 kV was struck in the chamber with a 20 standard cubic centimeters per min flow of oxygen for 5 min.

Aminosilanization was performed in the CVD system with a process temperature of 150° C. The chips were first dehydrated with two pump/purge cycles of the chamber with high-purity nitrogen. An oxygen plasma cleaning was then performed using the procedure described above. The surface was then rehydrated by injection of water vapor at a pressure of 0.5 Ton and soaked for 5 min. Then, 1 mL of APTES was vaporized and injected into the chamber at a pressure of 1.4 Ton and allowed to soak for 5 min. Spectroscopic ellipsometry measurements on SiO2-coated reference chips indicate that a highly reproducible 0.5-nm-thick silane layer is deposited with this process.

EXAMPLE 1 Electroosmosis Flow Rates

pnc-Si membrane chips with different amounts of freestanding membrane (one, three, six, or nine 200×200-μm windows) were fabricated as described in Methods (see FIG. 3). Characterization by electron microscopy determined that membranes had an average pore size of 19.5 nm and a porosity of 5.7% (see FIGS. 5 and 6).

An electroosmosis testing device was built by milling vertical wells into two pieces of polyethylene terephthalate (PET) (See FIG. 7). Access points were drilled into the side of the two PET blocks, each with a recessed ledge to hold an O-ring. pnc-Si membranes were placed between viton O-rings at the two access points and the devices were sealed using screws with wing nuts. Experiments were performed with 100 mM KCl, as some (although not all) embodiments of the present invention are envisioned as a pump for microfluidic chips and molecules that may in at least some instances require physiological salt concentrations. A Hewlett Packard E3612A dc power supply was used to apply a constant voltage of 20 V, and the volume of aqueous KCl passed into the receiving chamber was measured on a balance at specific time intervals. The supply chamber was continuously replenished so that pressure gradients between the two chambers were negligible. The chamber was open to atmosphere to prevent trapping of bubbles at the membrane caused by electrolysis at the platinum electrodes. Control experiments with solid silicon chips confirmed that the chambers were well sealed with no leakage current. Control experiments using chips with freestanding membranes removed did not exhibit any flow (See FIG. 8), indicating that the pores in the material are necessary for electroosmosis in some embodiments.

Representative volume vs. time curves are plotted in FIG. 8 for the four chips with different active membrane areas. Volumetric electroosmotic flow rates were determined from the slope of these curves. As shown in FIG. 9, the relationship between volumetric flow rate and active area in this particular instance is linear. In this non-limiting example, because an increase in active area results in a proportional increase in the number of pores, maximizing the active membrane area occupying a channel cross-section will maximize flow rates. Although the active areas are small compared with other EOPs, this active area is scalable using photolithography techniques and can be fabricated to match channel dimensions in non-limiting embodiments of the present invention. In various non-limiting embodiments, the active area will be at least 25%, at least 50%, at least 75% or 100% of the cross-sectional area of the fluid channel or channels associated with the EOP. Even in the small size formats shown in FIG. 3, pnc-Si membranes achieved flow rates up to 10 μL/min with an active area of 0.36 mm².

EXAMPLE 2 Theoretical Comparison

The following is a comparison of our experimental results from the above experiment to Rice—Whitehead theory for electroosmosis in narrow pores. Volumetric electroosmotic flow, V, through a narrow capillary in the absence of an external pressure gradient may be described by the following:

$\begin{matrix} {{V = {- {\frac{{\varepsilon\zeta}\; E_{z}A_{c}}{\eta}\left\lbrack {1 - \frac{2\; {I_{1\;}\left( {\kappa \; a} \right)}}{\kappa \; {{aI}_{0}\left( {\kappa \; a} \right)}}} \right\rbrack}}},} & \lbrack 1\rbrack \end{matrix}$

where ε is the product of the dielectric constant of the solution and the permittivity of free space, ξ the zeta potential of the capillary walls, E_(z) the electric field through the capillary, A_(c) the cross-sectional area of the capillary, η the viscosity, a the capillary radius, and I₀ and I₁ modified Bessel functions of the zeroth- and first order, respectively. K is the reciprocal of the Debye length and is found using

$\begin{matrix} {{\kappa^{- 1} = \sqrt{\frac{\varepsilon \; {kT}}{2\; q^{2}N_{A}c}}},} & \lbrack 2\rbrack \end{matrix}$

where k is the Boltzmann constant, T the temperature, q the charge of an ion in a symmetrical salt, N_(A) Avogadro's number, and c the concentration of the counterion (in mol/m³). The multiplier on the right-hand side of Eq. 1 takes into account the reduction in electroosmotic velocity of the region within the diffuse layer at the edge of the pore wall, although if κ⁻¹<<a, this term vanishes and the equation reduces to the classical Helmholtz—Smoluchowski description of electroosmosis. In our case, the nanopores within the membrane are similar in dimension to the Debye length and we consider this scaling factor. As this theory is developed using the Debye—Hiickel approximation, it is applicable for zeta potentials of up to 50 mV, and EOPs with higher zeta potentials require alternate solutions. As shown below, the magnitude of zeta potential for this embodiment of pnc-Si is less than 30 mV and so the Debye-Hückel approximation is valid for this embodiment.

Volumetric electroosmotic flow through a porous medium can be determined by expanding Eq. 1 to describe a bundle of capillaries in a manner similar to the use of Darcy's law for pressurized flow. Because we can obtain pore distributions from TEM images that are representative of the entire membrane area, we can sum Eq. 1 over all of the pores in the image and scale by the ratio of membrane area to image area, A_(tot)/A_(im), to obtain a total volumetric flow,

$\begin{matrix} {V_{tot} = {\frac{A_{tot}}{A_{im}}\frac{\varepsilon \; \zeta \; E_{z}}{\eta}{\sum\limits_{i = 1}^{\# \; {of}\mspace{11mu} {pores}}\; {\pi \; {{a_{i}^{2}\left\lbrack {1 - \frac{2\; {I_{1}\left( {\kappa \; a_{i}} \right)}}{{\kappa \; a_{i}{I_{0}\left( {\kappa \; a_{i}} \right)}}\;}} \right\rbrack}.}}}}} & \lbrack 3\rbrack \end{matrix}$

Rice-Whitehead theory gives the following expression for current I in a system with electroosmotic flow but lacking pressurized flow:

$\begin{matrix} {{I = {E_{z}A_{c}\lambda \left\{ {1 - {\beta \left\lbrack {1 - \frac{2\; {I_{1}\left( {\kappa \; a_{i}} \right)}}{\kappa \; a_{i}{I_{0}\left( {\kappa \; a_{i}} \right)}} - \frac{I_{1}^{2}\left( {\kappa \; a_{i}} \right)}{I_{0}^{2}\left( {\kappa \; a_{i}} \right)}} \right\rbrack}} \right\}}},} & \lbrack 4\rbrack \end{matrix}$

where β is (ε²ξ²κ²)/(16π²ηλ). At the physiological salt concentrations used in the experiments, β is very small and the electric field for the porous membrane is

$\begin{matrix} {{E_{z} = \frac{I}{A_{tot}{\chi\lambda}}},} & \lbrack 5\rbrack \end{matrix}$

where χ is the membrane porosity and λ is the conductivity of the solution. Experimental currents were found using a TEK DMM252 multimeter (Tektronix). Conductivity was measured with a CONE conductivity meter (Oakton Instruments) in bulk solution. We note that this measurement for the conductivity is an approximation, as the conductivity inside the nanopores could potentially deviate from the bulk solution. The results indicate electric fields of 8×10⁵ V/m across the membranes. These high electric fields are likely obtained for relatively low applied voltages because pnc-Si is only 15 nm thick. Because electroosmotic flow rates increase in proportion to the electric field strength (Eq. 1), high electric fields across the membrane enhance pump performance in this example. The benefit of using thin materials for electroosmosis in some instances is further examined in our following comparison with other EOPs.

The zeta potential of the pore walls was determined from streaming potential measurements. In these experiments, pnc-Si chips were inserted into the polycarbonate streaming potential device in FIG. 10 and were sealed by threading the two chambers together and compressing two O-rings. Ag/AgCl electrodes were prepared using the method of Burns and Zydney (described in Burns D B, Zydney A L (2000) Buffer effects on the zeta potential of ultrafiltration membranes. J Member Sci 172(1):39-48) and sealed into the device with silicon cord compressed with a polycarbonate screw. The chamber was filled with 100 mM KCl and pressurized with N₂ through an entry port fitted with Tygon tubing. For each measurement the pressure was allowed to stabilize for 30 s, as displayed by a VWR digital manometer, and the potential difference across the membrane was measured with a multimeter.

Streaming potential can be described using Rice—Whitehead theory, and if β once again is very small, we can use the expression

$\begin{matrix} {{\frac{E_{s}}{P} = {\frac{\varepsilon \; \zeta}{\eta \; \lambda}\left\lbrack {1 - \frac{2\; {I_{1}\left( {\kappa \; a} \right)}}{\kappa \; a\; {I_{0}\left( {\kappa \; a} \right)}}} \right\rbrack}},} & \lbrack 6\rbrack \end{matrix}$

where E_(s) is the streaming potential measured at zero current and P is the applied pressure through the membrane. In Eq. 6 the pore size a is taken to be the average pore size. The slope of a streaming potential versus pressure plot can be substituted for the left-hand side of Eq. 6, allowing for the determination of the zeta potential (see FIG. 12). By this method we find that the zeta potential of untreated pnc-Si membranes is −13.9 mV in this particular example, consistent with a native oxide surface.

Theoretical flow rates for each experiment were calculated using the electric field (Eq. 5), average zeta potential (Eq. 6), and pore characteristics as obtained from image processing of TEM micrographs. The theoretical flow rates are very similar to the experimental flow rates, indicating that theory developed for infinitely long pores also holds for pore radii that are on the same order as their length. If entrance and exit effects exist for electroosmosis in short nanopores, they were not observable by our methods in this particular example.

EXAMPLE 3 Surface Modifications

Modifying the surface of a material can in some instances change the zeta potential and alter the rate of electroosmotic flow. To investigate the ability to change the rate of electroosmosis through surface modifications, we treated pnc-Si membranes with both plasma oxidation and aminosilanization (see FIG. 13). Oxidation increased flow rates by about two times over the untreated samples, whereas aminosilanization reduced the flow rates almost to zero.

The effects of plasma oxidation can be understood as an enhancement of the intrinsic negative charge of pnc-Si. pnc-Si is expected to grow a negatively charged native oxide as silicon surfaces typically do in many instances in the presence of oxygen. This expectation is consistent with the negative zeta potential of untreated pnc-Si and the fact that electroosmostic flow is directed toward the negative electrode. Plasma oxidation, a treatment that is commonly used to remove carbonaceous substances from inorganic surfaces, has been previously shown to slow the diffusion of negatively charged molecules, indicating a stronger negative charge than untreated membranes. Treatment in oxygen plasma has been shown to create negatively charged silanol groups on the surface of poly (dimethyl siloxane) microfluidic channels, thereby allowing them to generate electroosmotic flow. In the pnc-Si membranes used in this example, plasma oxidation resulted in a larger measured zeta potential compared with untreated membranes (see FIG. 14), suggesting that the oxide layer formed during this process is denser than the native oxide layer.

Aminosilanization treatment causes a reduction of electroosmotic flow by reducing the native surface charges on pnc-Si. Silanization, a chemical reaction that enables a silicon-containing organic compound (or silane) to be covalently bonded to a silica surface, allows for a myriad of functionalization possibilities due to the abundance of silanes. Previous work with capillary electrophoresis and microfluidic chips has shown that surface modification with various silanes reduces the electroosmotic flow rates and the zeta potential of silica. In this example, we have grafted aminopropyltriethoxysilane (APTES) to the surface of the plasma-oxidized pnc-Si membranes. This modification results in a terminal amino group on the surface that carries a positive charge at neutral pH. The aminosilanization treatment greatly reduced the rate of electroosmosis, but did not change the direction of fluid flow or reverse the sign of the zeta potential (see FIGS. 13 and 14). This suggests that the positive amino groups in this example reduced the net surface charge within the pores, but that the modification was not complete enough to invert the native negative charge.

Note that in this example we calculated zeta potential from streaming potential (Eq. 6) and electroosmosis measurements (Eq. 3). Streaming potential measurements are a common form of zeta potential calculation, although we include electroosmotic calculations for comparison. pH changes induced by electrolysis at the electrodes and the effects of ion migration through the device can influence the zeta potential in some instances as calculated from electroosmosis. In this example, we do see an agreement in the trend of the zeta potentials as calculated by the different methods for the treated membranes, although electroosmosis calculations lead to lower zeta potentials for all membrane types in many instances.

EXAMPLE 4 Intrinsic Electroosmotic Flow Rate

pnc-Si may be in some instances more than 100 times thinner than other membrane materials used for dc electroosmotic pumping, and it may be expected that thinner materials in at least some instances would result in higher electroosmotic flow rates. However, the test devices used in this example were not optimized and thus do not take advantage of the intrinsic rate of electroosmosis for this material. Here, we calculate this potential rate by normalizing the flow rate by active area and transmembrane voltage. Note that only a small portion of the applied voltage V_(app) falls across the membrane. One method to determine the transmembrane voltage V_(TM) is through the electrical resistance in the system,

V _(app) =V _(dec)+(2R _(b) +R _(c) +R _(m))I.   [7]

The resistance R_(b) occurs within the bulk fluid in the chambers, R_(c) is the resistance of the orifice within the silicon chip, and R_(m) is the resistance of the membrane. V_(dec) is the decomposition potential, or the voltage required to initiate electrolysis at the Pt electrodes. The transmembrane voltage is the product of the membrane resistance and current: V_(TM)=R_(m)I. Current-voltage (I-V) curves (see FIG. 15, inset) can be used to determine the parameters in Eq. 7; the slope of an I-V curve of a system with an intact membrane gives (2R_(b)+R_(c)+R_(m)) and the slope of an I-V curve using an equivalent geometry chip in which the membrane was removed gives (2R_(b)+R_(c)). Thus, the difference in resistances calculated in these two cases is attributed to the membrane itself (R_(m)).

FIG. 15 illustrates the resistances as calculated from I-V curves for different active area chips both with and without membranes. In each case the difference is within the SE of the measurements (˜60Ω), indicating that the transmembrane voltage is no greater than 600 mV given experimental currents of 10 mA in this particular example. However, the actual transmembrane voltage appears to be much smaller than this estimate. The electric field strength (8×10⁵ V/m) and a 15-nm-thick membrane require a transmembrane voltage of only 12 mV. Low membrane resistance compared with all other resistances in the system has been observed for diffusive transport through pnc-Si. In some studies, the ultrathin dimension of the membrane results in a transmembrane resistance to diffusion that can be neglected compared with bulk resistances. Analogously, the low electrical resistance of pnc-Si in electroosmosis experiments follows from the ultrathin quality of the membrane, as other resistances in the system are much higher by comparison. It is striking that the insertion of a vanishingly thin membrane is necessary to generate microscale flow, yet does not significantly alter the current or power consumed by the system.

For this example, we have normalized the electroosmosis flow rate by the calculated transmembrane voltage and the active area of the chip to obtain a figure of merit of 260 mL·min⁻¹·cm⁻²·V⁻¹. In other non-limiting examples, the figure of merit may be in the range of 100-600 mL·min⁻¹·cm⁻²·V ¹. FIG. 16 shows that this figure of merit exceeds low-voltage EOPs fabricated from examples of porous silicon, alumina, and track-etched polymer by three orders of magnitude. Normalized flow rates for examples of ultrathin pnc-Si EOPs are also 20 times higher than carbon nanotube (CNT) EOPs, which are considered to have unique properties due to a slippery surface. Recent advances in alternating current (ac) electrode arrays have enabled the development of ac EOPs. Whereas the flow rates of ac EOPs increase nonlinearly compared with dc EOPs, at the low voltages used in this paper the figure of merit for pnc-Si EOPs exceeds that of an ac EOP by 70 times. In addition, electroosmotic flow through ac EOPs is hampered by high salt (>10 mM), which reduces their utility in solutions with physiological ionic concentrations. pnc-Si EOPs are also inexpensive to fabricate (˜$1 per chip), as hundreds of functioning membrane chips can be produced per 6-inch wafer.

The low electrical resistances and high electrical fields achieved across the ultrathin pnc-Si membranes enable the high normalized flow rate. To realize the full potential of pnc-Si-based EOPs, in some instances, fluidic channel cross-sections and active membrane areas may be of similar dimensions. In some instances, both the fluidic channel and active membrane cross-sectional width or diameter may be similar and in the range of 1 μm to 1 cm. Electrodes also could be brought closer to one another (e.g. spaced approximately 50-500 μm apart) or sputtered directly on the membrane surface to further minimize the applied voltage. Unlike ac EOPs, Faradaic reactions in dc EOPs can cause sample or fluid contamination, and this drawback could be a greater problem for smaller scale EOPs with electrodes closer to the membrane surface. By keeping the applied voltages low and using Ag/AgCl electrodes, we can minimize, in at least some embodiments, electrolysis and bubble formation within the pores of smaller scale EOPs.

EXAMPLE 5 Development of pnc-Si EOP Prototype

To demonstrate the applicability of pnc-Si membranes as pumps in microfluidic systems, we designed and tested an example prototype of a low-voltage EOP (see FIGS. 17 and 18). Ag/AgCl electrodes were prepared by coating 200-μm-diameter silver wire with Ag/AgCl ink (Conductive Compounds), which were allowed to dry before insertion into the device. The electrodes were sealed in the polycarbonate enclosure with silicone gaskets, and 500-μm-diameter tubing was connected to the inlet and outlet ports. The device was filled with 100 mM NaCl under vacuum. A double-slit pnc-Si membrane was inserted into the device between two viton O-rings in solution at atmospheric pressure. Once assembled, the device was left submerged in solution for at least 12 h before testing.

Both Ag/AgCl electrodes of the EOP were connected to an Agilent 33220A arbitrary waveform generator, which was used as a controllable voltage source. The current measurement was performed by using an Agilent 34410A digital multimeter. Both waveform generator and digital multimeter were connected to a personal computer and controlled remotely. This software, written in C/C++, was developed specifically to provide a constant dc voltage ranging from −5 V to +5 V and simultaneously record the current readouts from the multimeter.

Electroosmosis was visualized by tracking the movement of the menisci in inlet and outlet capillary tubes under a microscope equipped with a CCD camera. FIGS. 19-21 show images of the menisci at three different time points during an experiment in which the voltage polarity was switched every 40 s. The fluid flowed toward the negatively charged electrode at a rate of 1 μL/min at an applied voltage of 2 V (see FIG. 22). With the Ag/AgCl electrodes, fluid flow through the capillary tubes was achieved at voltages lower than the hydrolysis of water, and no gases were generated in the chamber during the experiments.

EXAMPLE 6 Thermodynamic Efficiency

We tested the capability of an EOP to pump against back pressures supplied by a precision air pressure regulator type 70 (Marsh Bellofram). Electroosmosis flow rates in the presence of back pressure were measured from the meniscus movement in the inlet tube (see FIGS. 23-24). Application of pressure linearly reduced the electroosmotic flow rate for applied voltages of 1,000-1,500 mV (See FIG. 23). In FIG. 25 we show the maximum flow rate at zero pressure Q., the maximum pressure at zero flow P., and the power consumption. Q. and P. can be used to normalize the flow rate and pressure, respectively, which is plotted in FIG. 24. This data compares well with the accepted relationship between flow rate and pressure,

$\begin{matrix} {{\frac{Q}{Q_{\max}} = {1 - \frac{P}{P_{\max}}}},} & \lbrack 8\rbrack \end{matrix}$

which is plotted as a solid line in FIG. 24.

The thermodynamic efficiency is the ratio of hydraulic to electrical power for an EOP, or

$\begin{matrix} {\eta = {\frac{1}{4}{\frac{Q_{\max}P_{\max}}{{IV}_{app}}.}}} & \lbrack 9\rbrack \end{matrix}$

Using the data from the back pressure analysis and the applied voltages, we calculated the thermodynamic efficiencies to be on the order of 0.00075% in this example. Thermodynamic efficiency has been shown to range from 0.005% to 2% experimentally in aqueous buffers. In embodiments of the present invention, the thermodynamic efficiency could be improved by orders of magnitude by moving the electrodes to either side of the membrane. The efficiency may also be improved by increasing the amount of membrane occupying the channel cross-section (currently 5% or less). Increasing the active area will raise both the flow rate and the current, but the current increase is expected to plateau as the resistance does (see FIG. 15).

To address whether the low back pressures supported by pnc-Si EOPs were related to membrane thickness, we conducted experiments with both 15- and 30-nm membranes. Surprisingly, we discovered that the 30-nm membranes exhibited lower stall pressures than the 15-nm membranes (see FIG. 25), indicating that thickness was not the only variable that determined stall pressures. By characterizing the pore distributions of the two membranes, we were able to calculate a significantly higher hydraulic permeability for the 30-nm membrane (see FIG. 26). Whereas the porosities of the 15- and 30-nm membranes were similar, it has been shown that larger pores naturally form in thicker membranes due to looser geometric constraints. Thus, the low stall pressure seen with pnc-Si may be directly related to the permeability. Low porosity, rather than greater thickness, may be the most effective way to improve this aspect of pnc-Si performance in some instances. Despite a low thermodynamic efficiency and low stall pressures in some of the current embodiments described, pnc-Si EOPs were used to produce flow rates of 1 μL/min through 10 cm of microcapillary tubing in voltages lower than 2 V. Thus, by installing pnc-Si EOPs in microfluidic chips with low back pressures, high microfluid flow rates can be achieved under low applied voltages (e.g. in the range of 0.02 μL/min-1 mL/min depending on the diameter of the fluid channel). pnc-Si could therefore find uses as in-line pumps to move reagents and samples between locations within microfluidic chips.

Summary of Examples

Examples of ultrathin pnc-Si membranes have been described that operate as high-flow-rate EOPs with low applied voltages. In at least some instances, this may be due to the small electrical resistance presented by the membrane and high electric fields across the molecularly thin membrane. The normalized flow rates of these examples were shown to be 20 times to several orders of magnitude higher than recent low-voltage EOPs. Pore distributions of pnc-Si membranes can be imaged via TEM, and we show using Rice—Whitehead theory that flow rates can be predicted for a given membrane in at least some instances. Surface modification through oxidation and silanization techniques may be used to change the zeta potential of the material and the electro-osmotic flow rates. The example of a prototype pnc-Si EOP described above has been shown to produce flow through capillary tubing with applied voltages as low as 0.25 V, although stalling pressures were in the range of 1 kPa. In some instances, such an EOP may be optimized by bringing the electrodes closer to the surface and maximizing active membrane area to channel dimensions. Due to scalable silicon fabrication methods, pnc-Si EOPs may be fabricated cheaply in at least some instances and can be easily integrated on silicon- or silica-based microfluid chips in at least some instances. pnc-Si EOPs will potentially enable low-voltage, on-chip electroosmotic pumping in microfluidic devices.

It will be appreciated that variants of the above-disclosed and other features and functions, or alternatives thereof, may be combined into many other different systems or applications. Various presently unforeseen or unanticipated alternatives, modifications, variations, or improvements therein may be subsequently made by those skilled in the art which are also intended to be encompassed by the following claims. 

We claim:
 1. A micro-fluidics device comprising a micro-fluid input, a micro-fluid output and an electroosmotic pump in fluid communication with the micro-fluid input and output, the electroosmotic pump including a nano-porous membrane having a thickness of 2-100 nm, the electrosmotic pump configured to move a fluid through the nano-porous membrane from the micro-fluid input into the micro-fluid output.
 2. The micro-fluidics device of claim 1, wherein the nano-porous membrane includes pores having widths in the range of 2 nm-100 nm.
 3. The micro-fluidics device of claim 1, wherein the thickness of the nano-porous membrane is in the range of 5-40 nm.
 4. The micro-fluidics device of claim 1, wherein the nano-porous membrane is a nano-porous membrane comprising silicon.
 5. The micro-fluidics device of claim 4, wherein the nano-porous membrane is a nano-porous membrane comprising silicon nitride.
 6. The micro-fluidics device of claim 1, wherein the nano-porous membrane is a porous nanocrystaline silicon membrane.
 7. The micro-fluidics device of claim 6, wherein the electroosmotic pump comprises a substrate, a passage extending through the substrate, and the porous nanocrystaline silicon membrane being over the passage extending through the substrate.
 8. The micro-fluidics device of claim 7, further comprising a plurality of passages extending through the substrate and one or more porous nanocrystaline silicon membranes over the plurality of passages.
 9. The microfluidics device of claim 7, wherein the substrate comprises a silicon substrate.
 10. The micro-fluidics device of claim 1, wherein the electroosmotic pump is configured to move the fluid through the nano-porous membrane at an applied voltage between 10 mV and 50 V.
 11. The micro-fluidics device of claim 1, wherein the nano-porous membrane comprises a zeta potential of approximately -5 mV to -40 mV.
 12. The micro-fluidics device of claim 1, wherein the nano-porous membrane comprises a zeta potential of approximately 100 mV to -100 mV.
 13. The micro-fluidics device of claim 1, further comprising a fluid channel extending from the micro-fluid output, wherein the nano-porous membrane has an active area that is at least 25% of a cross-sectional area of the fluid channel.
 14. The micro-fluidics device of claim 13, wherein the active area is at least 75% of the cross-sectional area.
 15. A micro-fluidics device comprising a micro-fluid input, a micro-fluid output and an electroosmotic pump in fluid communication with the micro-fluid input and output, the electroosmotic pump including a nano-porous membrane having a thickness of 2-100 nm, the electrosmotic pump configured to move a fluid through the nano-porous membrane from the micro-fluid input into the micro-fluid output at a flow rate of 50-800 mL·min⁻¹·cm⁻²·V⁻¹, wherein cm corresponds to an active area of the nano-porous membrane and V corresponds to a transmembrane voltage of the nano-porous membrane.
 16. The micro-fluidics device of claim 15, wherein the electrosmotic pump is configured to move the fluid through the nano-porous membrane from the micro-fluid input into the micro-fluid output at a flow rate of 100-500 mL·min-1·cm-2·V-1.
 17. A method of moving a fluid in a micro-fluidic device, the micro-fluidic device comprising a micro-fluid input, a micro-fluid output and an electroosmotic pump comprising a nano-porous membrane having a thickness of less than 100 nm in fluid communication with the micro-fluid input and output, the method comprising: applying a voltage of less than 50 V across the nano-porous membrane; and in response to the applied voltage, moving a fluid through the nano-porous membrane at a normalized flow rate of 50-800 mL·min⁻¹·cm⁻²·V⁻¹, wherein cm corresponds to an active area of the nano-porous membrane and V corresponds to a transmembrane voltage of the nano-porous membrane.
 18. The method of claim 17, wherein the nano-porous membrane includes pores having widths in the range of 2 nm-100 nm and the thickness of the nano-porous membrane is in the range of 5-40 nm.
 19. The method of claim 17, wherein applying the voltage comprises applying a voltage of less than 1 V across the nano-porous membrane.
 20. A micro-fluidics device comprising a fluid reservoir, a sample input, and an electroosmotic pump in fluid communication with the fluid reservoir and the sample input, the electroosmotic pump including a nano-porous membrane having a thickness of 2-100 nm, the electrosmotic pump configured to move a fluid from the fluid reservoir through the nano-porous membrane to move a sample from the sample input through a portion of the micro-fluidics device.
 21. A micro-fluidics device comprising an electroosmotic pump, a cooling fluid, a heat source, and a heat sink, the electroosmotic pump including a nano-porous membrane having a thickness of 2-100 nm, the electrosmotic pump configured to move the cooling fluid past the heat source and to the heat sink. 